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Электронная библиотека Попечительского совета механико-математического факультета Московского государственного университета
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Yamaguchi F. - Curves and surfaces in computer aided geometric design |
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Предметный указатель |
Acceleration, normal 27
Acceleration, tangential 27
Adini's method 118 119
Approximation, B-spline- 233-336
Approximation, Bernstein- 169-232
APT system 3
Area of a surface 42 43 47 48
B-spline curve segment 233-334
B-spline curve segment, derivatives 309-311
B-spline curve segment, interpolation of a sequence of points 247 to 250 325-327
B-spline curve segment, matrix representation 327-329
B-spline curve segment, properties 311 312
B-spline curve type (1) 281 282
B-spline curve type (2) 283
B-spline curve type (3) 294-296
B-spline, B-spline function, approximation 233-336
B-spline, B-spline function, definition 270-273
B-spline, B-spline function, normalized 273
B-spline, B-spline function, properties 270-274 291-294
B-spline, B-spline function, recursive calculation 285-291
B-spline, B-spline function, relation to Bernstein basis 293 294
B-spline, B-spline function, variation diminishing property 294
Bernoulli - Euler law 135
Bernstein approximation 169-232
Bernstein approximation, derivatives 190
Bernstein approximation, properties 189-193
Bernstein approximation, smoothing effect 193
Bernstein basis function 183 189-193
Bernstein basis vector 195
Bernstein polynomial 174
Bezier curve segment 169-232
Bezier curve segment, connection 213 214
Bezier curve segment, derivatives 198 199
Bezier curve segment, finite difference representation 194 195
Bezier curve segment, increase of degree 204-209
Bezier curve segment, partitioning 209-212
Bezier curve segment, various representation 193-198
Bezier net 217
Bezier polygon 173
Bezier surface patch 216-232
Bezier surface patch, connection 221-226
Bilinear transformation 36
Binomial expansion 182 183
Binormal vector, unit- 28
Blending function 77
Boundary condition matrix 111
C-spline 139
Cartesian product surface patch 132 133
Cauchy's relation 19
Chaikin's algorithm 320-325
Characteristic net 217
Characteristic polygon 173
Circular arc, circle, approximation 78-80 177 178 243-245
Circular arc, circle, approximation by Bezier curve segments 177 178
Circular arc, circle, approximation by cubic B-spline curve segments 243 to 245
Circular arc, circle, approximation by Ferguson curve segments 78-80
Circular arc, circle, approximation error 80 178
Circular arc, circle, approximation, passing through 3 points 354 355
Common perpendicular, length 352 353
Condition for determining a tangent vector to a curve on a surface 48
Conic section 337-346
Connection of Bezier curve segments 213 214
Connection of Bezier surface patches 221-226
Connection of Coons bi-cubic surface patches 96 97 107-109
Connection of curve segments 33-35
Connection of Ferguson surface patches 89-91
Connection of surface patches 57-59
Continuity, clss - 20 44
Control point 16
Convex combination 171 241 274
Convex hull property 241 311
Crease 15
Cross partial derivative vector 98 112-122
Cubic spline curves 145-160
Cubic spline curves, using circular arc length 159 160
Curvature 24-27
Curvature of a surface 49-51
Curvature vector 24-27
Curvature, average(mean) 51
Curvature, Gauss- 51
Curvature, normal 50
Curvature, principal 51
Curvature, radius 25
Curvature, total 51
Curve defining polygon 173
Curve generation by geometric processing 320-325
Curve segment, B-spline 233-334
Curve segment, Bezier- 169-232
Curve segment, conic section 337-346
Curve segment, cubic B-spline 233-251
Curve segment, cubic B-spline, geometrical relations among derivatives 342 343
Curve segment, cubic Bezier 169-182
Curve segment, cubic/cubic rational polynomial 346 347
Curve segment, Ferguson- 73-80
Curve segment, Hermite- 72-86
Curve segment, increase of degree 85 86 204-209
Curve segment, Lagrange- 64-71
Curve segment, non-uniform B-spline- 296
Curve segment, rational polynomial 337-350
Curve segment, T-comc 347-350
Curve segment, uniform cubic B-spline 233-251
Cusp 15
Cusp by cubic B-spline curve segments 245
De Boor's algorithm 312-315
Degeneration of a surface patch 44
Degeneration, formation of triangular surface patch 59 to 61
Derivatives of B-sphne curve segments 309-311
Derivatives of Bernstein polynomials 198 199
Derivatives of Bezier curve segments 198 199
Descartes' sign rule 192
Determination of a point by linear operations 199-204
Determination of a point on a B-sphne curve segment by linear operations 312-315
Determination of a point on a cubic Bezier curve segment 178 179
Divided difference 67
Divided difference, interpolation formula with remainder (Newton's formula) 68
ellipse 340
Equation of a normal plane 23
Equation of a plane passing through 3 points 353
Equation of a straight line segment 351
Equation of a tangent plane 46
Equation of an osculating plane 23
Error in approximating a circle 80 178
Finite difference, computation 32 33
Finite difference, determination of a point, on a curve 32 33
Finite difference, determination of a point, on a surface 51-55
Finite difference, matrix 33 52-55
Finite difference, operator 32
Finite difference, representation of a Bezier curve segment 194 195
First fundamental matrix of a surface 46-48
FMILL 89
Forrest's method 117
Frenet frame 29
Frenet - Serret formula 31
Function, B-spline- 236 237 270-273
Function, Bernstein basis- 182 183 189-193
Function, blending- 77
Function, Coons blending- 77
Function, full spline basis- 291
Function, Hermite- 72-83
Function, truncated power- 138
Function, uniform B-spline- 296
Functional determinant 44
Gauss curvature 51
Gauss quadrature 42
Hermite interpolation 72-134
Hermite polynomial 72 -134
Hyperbola 340
Increase of degree of a Bezier curve segment 204-209
Increase of degree of a Ferguson curve segment 85 86
Independence of coordinate axes 12-14
| Interpolation, Hermite- 72-134
Interpolation, Lagrange- 64-71
Interpolation, of a sequence of points by a B-sphne curve 247-250 325-327
Interpolation, spline- 135-168
Intersection of 2 curves 43 44
Intersection of 3 planes 354
Intersection of a curve and a plane 43
Invariance of shape under coordinate transformation 18 19
Inverse transformation of a uniform cubic, B-sphne curve 247-250 325-327
Jacobian 44 60-62
Knot, additional 272
Knot, extended 272
Knot, insertion 316-320
Knot, interior 272
Knot, multiple 291
Knot, pseudo 292
Kronecker delta 92
Lagrange's formula 65
Leibnitz' formula 356
Length of a curve 42
Length of a curve, on a surface 47
Length of common perpendicular 352 353
Line segment by a Bezier curve segment 176 177
Line segment by a cubic B-spline curve segment 243
Line segment, perpendicular bisector 351
Local uniqueness 242
Marsden's identity 358 359
Mathematical model 3 4
Matrix representation of a B-spline curve segment 327-329
Matrix, boundary condition- 111
Matrix, finite difference- 33 52-55
Matrix, first fundamental- (of a surface) 46-48
Matrix, second fundamental- (of a surface) 50
Minimal interpolation property 140-144
Model, mathematical 3 4
Model, physical 3 4
Moving frame 29
Net, surface defining- 217
Normal plane 23
Normal plane, equation 23
Normal vector, unit- 46
Normal, principal- 23
Normalized B-spline 273
Offset surfaces 63
Order of spline 136
Ordinary point 20
Osculating plane 23
parabola 342
Parametric cubic curve 31
Parametric representation of a curve 20
Parametric representation of a surface 44
Partitioning of Coons bi-cubic surface patches 122 123
Partitioning of cubic Bezier curve segments 179-182
Partitioning of curve segments 39
Partitioning of Ferguson curve segments 84 85
Pentagonal surface 9 10
Perpendicular bisector of a line segment 351 352
Physical model 3 4
Plane curve, condition to be 29
Plane, normal 23
Plane, osculating 23
Plane, passing through 3 points 353
Plane, rectifying 24
Plane, tangent 46
Plane, vector representation 353
Point, control- 16
Point, inflection- 27
Point, knot- 240
Point, ordinary 20
Point, regular 20
Point, singular 20
Polynomial, Bernstein- 189
Polynomial, Lagrange- 65
Power basis vector 195
Principal normal, vector, unit- 46
Principle of minimizing total bending energy 136 140
Product of differences 64
Property, minimal interpolation- 140-144
Property, of B-spline curve segments 311 312
Property, of Bernstein polynomials 189-193
Property, of Bezier curve segments 189-193
Property, variation diminishing- 192 294 312
Rectifying plane 24
Regular 20
Second fundamental matrix of a surface 50
Shape control, global 16 17
Shape control, local 16 17
Shape control, of a Coons bi-cubic surface patch 126-131
Shift operator 193 194
Singular point 20
SKETCHPAD 3 4
Space curve 14
Space curve, condition to be 29
Spatial uniqueness 11
SPLINE 135-168
Spline curve 145-160
Spline Function 136 137
Spline interpolation 135-168
Spline surface 163-168
Spline, basis- 160-163 270-273
Spline, bending rigidity 136
Spline, by Bezier curve segments 214-216
Spline, C-spline 139
Spline, end conditions of parametric- 151-159
Spline, fundamental 163
Spline, mathematical 136
Spline, minimal interpolation property 140-144
Spline, natural 138-144
Spline, periodic 159
Spline, physical 136
Spline, smoothing 144
Spline, stored bending energy 136
Spline, under tension 7
Subsphne basis 291
Surface of revolution 264
Surface of revolution by cubic B-spline curve segments 264-270
Surface patch, B-sphne- 334 335
Surface patch, Bezier- 216-226
Surface patch, bicubic Coons- 111 112
Surface patch, bilinear 100
Surface patch, Boolean sum type 133
Surface patch, Cartesian product 132
Surface patch, Coons-(1964) 91-101
Surface patch, Coons-(1967) 102-112
Surface patch, Ferguson- 87-91
Surface patch, general B-spline surface 334 335
Surface patch, loft 132
Surface patch, tensor product 132
Surface patch, triangular 228-231
Tangent plane 46
Tangent plane, equation 46
Tangent vector, unit- 21
Tangent, equation of a tangent line 21
Torsion 28
Torsion of a cubic curve 41
Transformation, bilinear 36
Transformation, homographic 36
Transformation, invariance of shape under coordinate- 18 19
Transformation, inverse 247-250 262-264 325-327
Transformation, inverse, curve 247-250 325-327
Transformation, inverse, surface 262-264
Transformation, parameter 35-39
Transformation, rational formula 36
Triangular area coordinate 229
Triangular surface patch 228-231
Triangular surface patch by degeneration 59 60 131 226-228
Truncated power function 138
Twist vector 91 98 104 112-116
Twist vector, method of determination 117 -122
Types of surfaces 132-133
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